Submitted:
07 October 2026
Posted:
09 October 2026
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Abstract
We study the m-generalized group inverse of Banach elements and establish several new properties. The main result is a novel characterization via the right hybrid (b,c)-inverse, revealing an intrinsic link between the two notions. Additive properties and image-based characterizations are also derived. These results extend the theory of the m-weak group inverse to a broader class of Banach elements and shed new light on infinite-dimensional operators.
Keywords:
weak group inverse
; m-weak group inverse
; g-Drazin inverse
; core-EP inverse
; Banach algebra
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